VIEWS: 195 PAGES: 16 POSTED ON: 4/10/2010 Public Domain
Test Topics Graph a sinusoid given equation in transformational form or functional form State mapping rule Given the mapping rule, state the transformations Given the mapping rule, state equation in functional or transformational form State transformations Given graph state equation as transformation of sine or cosine Given word problem graph and state equation State amplitude, period, phase shift, principal axis, local maximum, local minimum Transformational Functional 1 ( y VT ) sin 1 x HT y VS sin 1 x HT VT VS HS HS 1( y 6) sin 2 x 30 y 3sin 2 x 30 6 3 Transformations Rx No VT 6 VS 3 HS 1 period 180 2 HT 30 PA y 6 Mapping Rule x, y 1 x 30,3y 6 2 Word Problems Ferris Wheel A Ferris wheel has a diameter of 32 m, and its centre is 18 m above the ground. The wheel completes one revolution every 30 seconds. a) Graph a rider’s height above the ground (m) versus time (s) during a 2 minute ride. State any assumptions. b) Write an equation to model this relationship. c) State the domain and range of the function. Principal Axis A Ferris wheel has a diameter of 32 m, and its centre is 18 m above the ground. The wheel completes one revolution every 30 seconds. Amplitude – Vertical Stretch A Ferris wheel has a diameter of 32 m, and its centre is 18 m above the ground. The wheel completes one revolution every 30 seconds. Period A Ferris wheel has a diameter of 32 m, and its centre is 18 m above the ground. The wheel completes one revolution every 30 seconds. Horizontal Stretch HS = period 360 A Ferris wheel has a diameter of 32 m, and its centre is 18 m above the ground. = 30/360 The wheel completes one revolution every 30 seconds. = 1/12 Transformations Vertical Translation (Principal Axis) Vertical Stretch (Amplitude) Horizontal Stretch (Period/360) Horizontal Translation (Phase Shift) Reflection Write your own equation and graph Transformations Vertical Translation (18) Vertical Stretch (16) Horizontal Stretch (1/12) Horizontal Translation (0) Reflection (Yes) Which equation do you choose? 1 ( y 16) sin 1 x 18 12 1 ( y 18) cos(12 x) 16 1 ( y 18) sin(12 x) 16 1 ( y 18) sin(12 x) 16 1 ( y 18) sin(12 x) 16 Which graph makes sense? Why? 1 ( y 18) cos(12 x) 16 Domain=? Range =? Domain=? Range =? Domain = {x єR, x≥0} Range = {y єR, 2 ≤ y ≤ 34} Ocean Cycles A point on the ocean rises and falls as waves pass. Suppose that a wave passes every 4 s, and the height of each wave from the crest to the trough is 0.5 m. Sketch a graph to model the height of the point relative to its average height for a complete cycle. Use exact values to write an equation of the form h = a cos kt to model the height of the point, h meters, relative to its average height, as a function of time, t seconds. Paddle Steamer